# Comparative analysis of power-law type fin problem using wavelet collocation and Galerkin methods

## Authors

• Surjan Singh DST-CIMS BHU, Varanasi
• Subrahamanyam Upadhyay DST-CIMS BHU Varanasi, India
• K. N. Rai Department of Mathematical Sciences IIT BHU, Varanasi, India

2014-11-17

## Keywords:

Linear, non-linear, differential equation, fins, wavelet Galerkin, collocation method.

## Abstract

In this paper, Wavelet Collocation Method and Wavelet Galerkin Method have been used to evaluate the temperature distribution of a straight rectangular fin. The linear problem has been solved by Wavelet Galerkin Method while non-linear problem by Wavelet Collocation Method. It has been observed that accuracy increases as the number of basis function increases. The result thus obtained is compared with other available results obtained by using approximate analytic methods such as Adom ian Decomposition Method, Differential Transformation Method as well as exact solution. It has been observed that the result obtained by present method is exactly same as that obtained by exact method. The method provides a unique solution forÂ  n = -3/2, N= Â± 0.9 and n = -3, N = Â±0.4. The justification of unique solution gets confirmed from Figs. 7 and 8. The present method provides single solution for all existing values. The convergence analysis of the proposed method along side numerical procedure for this boundary value problem is given to test wider applicability and accuracy of the method.

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